# How do you write the equation  y= -3/2x + 4/3  in standard form?

Apr 13, 2017

See the entire solution process below:

#### Explanation:

The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

First, we will multiply each side of the equation by $\textcolor{red}{6}$ to eliminate the fractions because by the definition above all of the coefficients and the constant must be integers:

$\textcolor{red}{6} \cdot y = \textcolor{red}{6} \left(- \frac{3}{2} x + \frac{4}{3}\right)$

$6 y = \left(\textcolor{red}{6} \times - \frac{3}{2} x\right) + \left(\textcolor{red}{6} \times \frac{4}{3}\right)$

$6 y = \left(\cancel{\textcolor{red}{6}} 3 \times - \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} x\right) + \left(\cancel{\textcolor{red}{6}} 2 \times \frac{4}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}\right)$

$6 y = - 9 x + 8$

Now, we will add $\textcolor{red}{9 x}$ to each side of the equation to put this equation into standard form:

$\textcolor{red}{9 x} + 6 y = \textcolor{red}{9 x} - 9 x + 8$

$9 x + 6 y = 0 + 8$

$\textcolor{red}{9} x + \textcolor{b l u e}{6} y = \textcolor{g r e e n}{8}$